To a medium bowl, add honey, soy sauce, lemon juice, garlic, and red pepper flakes. Whisk to combine.
Place the shrimp in a large zip-top bag and pour in ⅓ of the sauce. (Reserve the rest of the sauce for later.) Seal the bag, removing as much air as possible. Massage the shrimp gently to coat them evenly. Refrigerate for at least 20 minutes, up to 2 hours.
When ready, to a large skillet over medium heat, add 1 tablespoon oil. Once hot, add the broccoli florets. Cook, stirring occasionally, until the broccoli is tender, about 5 minutes. Transfer the cooked broccoli to a plate and cover with aluminum foil to keep warm.
To the same skillet, add the remaining olive oil. Once hot, add the sausage and heat, turning occasionally, until browned on both sides, about 4-5 minutes.
Add the marinated shrimp to the skillet with the sausage. (Discard the marinade in the bag.) Cook for 1-2 minutes on each side, or until the shrimp are cooked through.
Pour the reserved sauce into the skillet and bring to a simmer. Cook for 3-5 more minutes, allowing the sauce to cook down slightly.
Add the cooked broccoli back to the skillet. Toss everything together until well-coated.
Serve over cooked white rice.